Problem: $f(t) = -2t^{2}-7t$ $g(t) = 7t^{2}+f(t)$ $ g(f(-2)) = {?} $
Solution: First, let's solve for the value of the inner function, $f(-2)$ . Then we'll know what to plug into the outer function. $f(-2) = -2(-2)^{2}+(-7)(-2)$ $f(-2) = 6$ Now we know that $f(-2) = 6$ . Let's solve for $g(f(-2))$ , which is $g(6)$ $g(6) = 7(6^{2})+f(6)$ To solve for the value of $g$ , we need to solve for the value of $f(6)$ $f(6) = -2(6^{2})+(-7)(6)$ $f(6) = -114$ That means $g(6) = 7(6^{2})-114$ $g(6) = 138$